Understanding place value

Last night I had an interesting realization about my son’s understanding of place value. It is clearly incomplete.

We were continuing our made-up story about Max, the 701 hundred year old 7 year old. He was cursed at the age of 7 to never age and to never die, and now he is 701 years old and working hard with his friends to try and break the curse.

At one point Max gives an explanation of curse to the sea elf king in order to ask the king for help and Max says how many years old he is. I left the actual number of years Max had been alive out of the story though and so my son filled it in.

“Max has been alive for six hundred and four years,” my son said.

“Oh, how did you get that?” I asked.

“Six hundred and three plus seven is seven hundred, so six hundred and four plus seven is seven hundred and one,” my son replied.

He spoke so confidently and assuredly that I did not correct him. Also, I wasn’t totally clear at that time exactly at that time what he was thinking, and it was late.

I think that he was regrouping the ten and confusing a regrouped ten as a one hundred. He did the same thing when he first tried counting on from 100 at age four. I remember quite clearly him counting 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 200. I also remember how stubbornly he continued with this understanding.

I know of some strategies that I can use to continue building his understanding of place value. I am not sharing this story to look for help or a diagnosis but just to point out that a child who the previous night confidently and accurately multiplied 400 by 21 in his head still has unresolved issues with place value.

I think my take-away is that I need to be cautious about what assumptions of knowledge I make about my son (and of course the same is true of my students).

“It’s 8400”

I had a fascinating exchange with my son last night. I was telling him a made up story, and at one point this character who is cursed and very old said that his age was “Four hundred times a score and one.” My son asked what a score was, and I told him twenty.

He then tried to figure out the person’s age. He started by asking what is four times twenty, and I told him he could figure that out. He counted up by fours to get eighty, and then said that four hundred times twenty is eight hundred. He thought for a moment and said that no, it must be eight thousand, which meant the final answer is eight thousand four hundred.

This makes me curious about how he understands the number twenty. He knows apparently that four hundred times something is one hundred times whatever four times the something is, although I am not clear he would explain it like that. However, he apparently did not use the fact that twenty times something is the same as ten times two times the something.